#989760 (C++17) No.977 アリス仕掛けの摩天楼

提出ソース

結果

問題	No.977 アリス仕掛けの摩天楼
ユーザー	👑 Nachia
提出日時	2024-06-20 19:19:00
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	38 ms / 2,000 ms
コード長	11,400 bytes
コンパイル時間	1,434 ms
コンパイル使用メモリ	114,100 KB
実行使用メモリ	9,472 KB
最終ジャッジ日時	2024-06-20 19:19:04
合計ジャッジ時間	3,109 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,812 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	1 ms 6,944 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	1 ms 6,940 KB
testcase_06	AC	1 ms 6,940 KB
testcase_07	AC	2 ms 6,944 KB
testcase_08	AC	1 ms 6,944 KB
testcase_09	AC	2 ms 6,940 KB
testcase_10	AC	1 ms 6,944 KB
testcase_11	AC	2 ms 6,940 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	5 ms 6,944 KB
testcase_14	AC	5 ms 6,940 KB
testcase_15	AC	5 ms 6,944 KB
testcase_16	AC	5 ms 6,944 KB
testcase_17	AC	4 ms 6,940 KB
testcase_18	AC	11 ms 6,944 KB
testcase_19	AC	11 ms 6,940 KB
testcase_20	AC	18 ms 6,940 KB
testcase_21	AC	25 ms 7,808 KB
testcase_22	AC	38 ms 9,216 KB
testcase_23	AC	36 ms 9,472 KB
testcase_24	AC	34 ms 9,344 KB
testcase_25	AC	35 ms 9,344 KB

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ソースコード

raw source code

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
#define repr(i,n) for(int i=int(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
using namespace std;

#include <cassert>

namespace nachia{

template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = std::move(items[i].second);
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};

} // namespace nachia

namespace nachia{


struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
        int xorval() const { return from ^ to; }
    };
    Graph(int n = 0, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    template<class Cin>
    static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){
        Graph res(n, undirected, m);
        for(int i=0; i<m; i++){
            int u, v; cin >> u >> v;
            res[i].from = u - offset;
            res[i].to = v - offset;
        }
        return res;
    }
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addNode() noexcept { return m_n++; }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
        m_n = newV;
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = newV[mapping[i]]++;
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};

} // namespace nachia

namespace nachia{

struct DfsTree{
    std::vector<int> dfsOrd;
    std::vector<int> parent;

    template<bool OutOrd>
    static DfsTree Construct(const CsrArray<int>& adj, int root = 0){
        DfsTree res;
        int n = adj.size();
        res.dfsOrd.resize(n);
        int Oi = 0;
        std::vector<int> eid(n, 0), parent(n, -2);
        for(int s=root; Oi<n; s == n-1 ? s=0 : ++s) if(parent[s] == -2){
            int p = s;
            parent[p] = -1;
            while(0 <= p){
                if(eid[p] == (OutOrd ? (int)adj[p].size() : 0)) res.dfsOrd[Oi++] = p;
                if(eid[p] == (int)adj[p].size()){ p = parent[p]; continue; }
                int nx = adj[p][eid[p]++];
                if(parent[nx] != -2) continue;
                parent[nx] = p;
                p = nx;
            }
            s++; if(s == n) s=0;
        }
        res.parent = std::move(parent);
        return res;
    }
    template<bool OutOrd>
    static DfsTree Construct(const Graph& g, int root = 0){ return Construct<OutOrd>(g.getAdjacencyArray(), root); }
};

} // namespace nachia

namespace nachia{

struct TwoEdgeConnectedComponents{
    Graph mG;
    int m_numComponent;
    std::vector<int> m_color;
    TwoEdgeConnectedComponents(Graph G = Graph(0, true)){
        assert(G.isUndirected());
        int n = G.numVertices(), m = G.numEdges();
        if(n == 0){ mG = G; m_numComponent = 0; return; }
        std::vector<int> P, ord, I(n); {
            auto dfsTree = DfsTree::Construct<false>(G);
            P = std::move(dfsTree.parent);
            ord = std::move(dfsTree.dfsOrd);
            for(int i=0; i<n; i++) I[ord[i]] = i;
        }
        std::vector<int> rev = I, PE(n, -1);
        for(int e=0; e<m; e++){
            int v = G[e].from, w = G[e].to;
            if(I[v] < I[w]) std::swap(v, w);
            if(P[v] == w && PE[v] < 0){ PE[v] = e; }
            else rev[v] = std::min(rev[v], I[w]);
        }
        for(int i=n-1; i>=0; i--){
            int v = ord[i], w = P[v];
            if(w >= 0) rev[w] = std::min(rev[w], rev[v]);
        }
        m_numComponent = 0;
        m_color.resize(n);
        for(int v : ord){
            if(rev[v] == I[v]) m_color[v] = m_numComponent++;
            else m_color[v] = m_color[P[v]];
        }
        mG = std::move(G);
    }
    int numComponents() const noexcept { return m_numComponent; }
    int operator[](int v) const { return m_color[v]; }
    CsrArray<int> getTeccVertices() const {
        int n = mG.numVertices();
        std::vector<std::pair<int, int>> res(n);
        for(int i=0; i<n; i++) res[i] = { m_color[i], i };
        return CsrArray<int>::Construct(numComponents(), res);
    }
    // bridge : -1
    std::vector<int> getEdgeMapping() const {
        std::vector<int> res(mG.numEdges(), -1);
        for(int i=0; i<mG.numEdges(); i++) if(m_color[mG[i].from] == m_color[mG[i].to]) res[i] = m_color[mG[i].from];
        return res;
    }
    std::vector<int> getVertexMapping() const { return m_color; }
};

}


namespace nachia {

struct DsuFast{
private:
    std::vector<int> w;
public:
    DsuFast(int n = 0) : w(n, -1) {}
    int leader(int u){
        if(w[u] < 0) return u;
        return w[u] = leader(w[u]);
    }
    int operator[](int u){ return leader(u); }
    int merge(int u, int v){
        u = leader(u);
        v = leader(v);
        if(u == v) return u;
        if(-w[u] < -w[v]) std::swap(u, v);
        w[u] += w[v];
        w[v] = u;
        return u;
    }
    int size(int u){ return -w[leader(u)]; }
    bool same(int u, int v){ return leader(u) == leader(v); }
};

} // namespace nachia

namespace nachia{

struct ConnectedComponents{
    ConnectedComponents(const CsrArray<int>& adj){
        int n = adj.size();
        DsuFast dsu(n);
        for(int v=0; v<n; v++) for(int w : adj[v]) dsu.merge(v, w);
        m_color.assign(n, -1);
        m_numC = 0;
        for(int i=0; i<n; i++) if(dsu.leader(i) == i) m_color[i] = m_numC++;
        for(int i=0; i<n; i++) m_color[i] = m_color[dsu.leader(i)];
    }
    ConnectedComponents(const Graph& G = Graph(0, true)){
        int n = G.numVertices();
        DsuFast dsu(n);
        for(auto e : G) dsu.merge(e.from, e.to);
        m_color.assign(n, -1);
        m_numC = 0;
        for(int i=0; i<n; i++) if(dsu.leader(i) == i) m_color[i] = m_numC++;
        for(int i=0; i<n; i++) m_color[i] = m_color[dsu.leader(i)];
    }
    int numComponents() const noexcept { return m_numC; }
    const std::vector<int>& getMapping() const { return m_color; }
    CsrArray<int> getCsr() const {
        std::vector<std::pair<int, int>> buf(m_color.size());
        for(int i=0; i<(int)m_color.size(); i++){
            buf[i] = std::make_pair(m_color[i], i);
        }
        return CsrArray<int>::Construct(numComponents(), std::move(buf));
    }
private:
    int m_numC;
    std::vector<int> m_color;
};

} // namespace nachia

void testcase(){
    int N; cin >> N;
    auto graph = nachia::Graph::Input(cin, N, true, N-1, 0);
    auto tecc = nachia::TwoEdgeConnectedComponents(graph).numComponents();
    auto cc = nachia::ConnectedComponents(graph).numComponents();
    if(cc == 1 || tecc <= 2){ cout << "Bob\n"; }
    else cout << "Alice\n";
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}

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結果

テストケース

ソースコード